The amino acid alphabet and the architecture of the protein sequence-structure map. I. Binary alphabets.

Ferrada E - PLoS Comput. Biol. (2014)

Bottom Line:
I characterize the properties underlying these differences and relate them to the structure of the potential.Among these properties are the expected number and relative distribution of sequences associated to specific structures and the diversity of structures as a function of sequence divergence.I study the types of binary potentials observed in natural amino acids and show that there is a strong bias towards only some types of potentials, a bias that seems to characterize the folding code of natural proteins.

Affiliation: Santa Fe Institute, Santa Fe, New Mexico, United States of America.

ABSTRACTThe correspondence between protein sequences and structures, or sequence-structure map, relates to fundamental aspects of structural, evolutionary and synthetic biology. The specifics of the mapping, such as the fraction of accessible sequences and structures, or the sequences' ability to fold fast, are dictated by the type of interactions between the monomers that compose the sequences. The set of possible interactions between monomers is encapsulated by the potential energy function. In this study, I explore the impact of the relative forces of the potential on the architecture of the sequence-structure map. My observations rely on simple exact models of proteins and random samples of the space of potential energy functions of binary alphabets. I adopt a graph perspective and study the distribution of viable sequences and the structures they produce, as networks of sequences connected by point mutations. I observe that the relative proportion of attractive, neutral and repulsive forces defines types of potentials, that induce sequence-structure maps of vastly different architectures. I characterize the properties underlying these differences and relate them to the structure of the potential. Among these properties are the expected number and relative distribution of sequences associated to specific structures and the diversity of structures as a function of sequence divergence. I study the types of binary potentials observed in natural amino acids and show that there is a strong bias towards only some types of potentials, a bias that seems to characterize the folding code of natural proteins. I discuss implications of these observations for the architecture of the sequence-structure map of natural proteins, the construction of random libraries of peptides, and the early evolution of the natural amino acid alphabet.

pcbi-1003946-g005: Association between non-degeneracy and encodability.For each potential sampled in this study, the plot shows non-degeneracy () versus encodability (c). Non-degeneracy corresponds to the fraction of genotype space that yields viable sequences; encodability, to the fraction of accessible conformations (see Models). Colors match the potentials types described in Fig. 3 and Table 1.

Mentions:
and are not independent and overall, correlate positively. Their association, however, depends on the type of potential (Fig. 5). In the case of potentials type I, II and IV, an increase in leads to larger c values. Potentials type III, however, preserve similar c despite large variation in . With the exception of few potentials type I and VI, maps induced by binary potentials, use a larger fraction of sequence than structure space (dashed line, Figure 5).

pcbi-1003946-g005: Association between non-degeneracy and encodability.For each potential sampled in this study, the plot shows non-degeneracy () versus encodability (c). Non-degeneracy corresponds to the fraction of genotype space that yields viable sequences; encodability, to the fraction of accessible conformations (see Models). Colors match the potentials types described in Fig. 3 and Table 1.

Mentions:
and are not independent and overall, correlate positively. Their association, however, depends on the type of potential (Fig. 5). In the case of potentials type I, II and IV, an increase in leads to larger c values. Potentials type III, however, preserve similar c despite large variation in . With the exception of few potentials type I and VI, maps induced by binary potentials, use a larger fraction of sequence than structure space (dashed line, Figure 5).

Bottom Line:
I characterize the properties underlying these differences and relate them to the structure of the potential.Among these properties are the expected number and relative distribution of sequences associated to specific structures and the diversity of structures as a function of sequence divergence.I study the types of binary potentials observed in natural amino acids and show that there is a strong bias towards only some types of potentials, a bias that seems to characterize the folding code of natural proteins.

Affiliation:
Santa Fe Institute, Santa Fe, New Mexico, United States of America.

ABSTRACTThe correspondence between protein sequences and structures, or sequence-structure map, relates to fundamental aspects of structural, evolutionary and synthetic biology. The specifics of the mapping, such as the fraction of accessible sequences and structures, or the sequences' ability to fold fast, are dictated by the type of interactions between the monomers that compose the sequences. The set of possible interactions between monomers is encapsulated by the potential energy function. In this study, I explore the impact of the relative forces of the potential on the architecture of the sequence-structure map. My observations rely on simple exact models of proteins and random samples of the space of potential energy functions of binary alphabets. I adopt a graph perspective and study the distribution of viable sequences and the structures they produce, as networks of sequences connected by point mutations. I observe that the relative proportion of attractive, neutral and repulsive forces defines types of potentials, that induce sequence-structure maps of vastly different architectures. I characterize the properties underlying these differences and relate them to the structure of the potential. Among these properties are the expected number and relative distribution of sequences associated to specific structures and the diversity of structures as a function of sequence divergence. I study the types of binary potentials observed in natural amino acids and show that there is a strong bias towards only some types of potentials, a bias that seems to characterize the folding code of natural proteins. I discuss implications of these observations for the architecture of the sequence-structure map of natural proteins, the construction of random libraries of peptides, and the early evolution of the natural amino acid alphabet.